Sequence and Series questions
1035 published questions with worked solutions.
- The number of terms common to the two A.P.'s 3,7,11, ,407 and 2,9,16, ,709 is
- If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4^ th A.M. is equal to 2^...
- The sum of first four terms of a geometric progression (G.P.) is 65 12 and the sum of their respective reciprocals is 65 18 . If...
- Let A_1,A_2,A_3, be squares such that for each n 1, the length of the side of A_n equals the length of the diagonal of A_ n+1 ....
- If the arithmetic mean and geometric mean of the p^ th and q^ th terms of the sequence -16,8,-4,2, satisfy the equation...
- Consider an arithmetic series and a geometric series having four initial terms from the set 11,8,21,16,26,32,4 . If the last...
- Let 1 16 , a and b be in G.P. and 1a, 1b,6 be in A.P., where a,b>0. Then 72(a+b) is equal to
- _ r=1 ^ 10 r! (r^3+6r^2+2r+5 )= (11!), then the value of is equal to
- Let a_n _ n=1 ^ be a sequence such that a_1=1, a_2=1 and a_ n+2 =2a_ n+1 +a_n for all n 1. Then the value of 47 _ n=1 ^ a_n 2^ 3n...
- If _32, _3 (2^x-5 ), _3 (2^x- 72 ) are in an arithmetic progression, then the value of x is equal to
- Let a_1,a_2, ,a_ 10 be an AP with common difference -3 and b_1,b_2, ,b_ 10 be a GP with common ratio 2. Let c_k=a_k+b_k, k=1,2,...
- If a_1(>0),a_2,a_3,a_4,a_5 are in a G.P., a_2+a_4=2a^1+1 and 3a_2+a_3=2a, then a_4+a^2+2a^4 is equal to
- If the sum of the first ten terms of the series 15+ 2 65 + 3 325 + 4 1025 + 5 2501 + is mn, where m and n are co-prime numbers,...
- Let for n=1,2, ,50, S be the sum of the infinite geometric progression whose first term is n^2 and whose common ratio is 1...
- Let 3,6,9,12, upto 78 terms and 5,9,13,17, upto 59 terms be two series. Then, the sum of terms common to both the series is equal...
- Let a_1=b_1=1, a_n=a_ n-1 +2 and b_n=a_n+b_ n-1 for every natural number n 2. Then _ n=1 ^ 15 a_n b_n is equal to
- The series of positive multiples of 3 is divided into sets: 3 , 6,9,12 , 15,18,21,24,27 , . Then the sum of the elements in the...
- 2^3-1^3 1 7 + 4^3-3^3+2^2-1^3 2 11 + 6^3-5^3+4^3-3^3+2^3-1^3 3 15 + + 30^3-29^3+28^3-27^3+ +2^3-1^3 15 63 is equal to
- Let x_1,x_2,x_3, ,x_ 20 be in geometric progression with x_1=3 and the common ratio 12. A new data is constructed replacing each...
- If _ k=1 ^ 10 k k^4+k^2+1 = mn, where m and n are coprime, then m+n is equal to
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